Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19128865 | C2 | semidirect |
| 2. C2×#19128852 | C2 | semidirect |
| 3. C22×#14581938 | C2 | semidirect |
| 4. #24923840 | C2 | semidirect |
| 5. #24923836 | C2 | semidirect |
| 6. #24923660 | C2 | semidirect |
| 7. #24923657 | C2 | semidirect |
| 8. #24923652 | C2 | semidirect |
| 9. #24923640 | C2 | semidirect |
| 10. #24923227 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 16. C2×Dic668 | C22 | semidirect |
| 17. C2×#14581940 | C22 | semidirect |
| 18. C2×#14581939 | C22 | semidirect |
| 22. C2×#14581938 | C22 | semidirect |
| 23. C2×#14581937 | C22 | semidirect |
| 24. C2×#14581935 | C22 | semidirect |
| 26. #19128830 | C22 | semidirect |
| 29. #19128819 | C22 | semidirect |
| 35. #19128742 | C22 | semidirect |
| 36. C8×Dic167 | C22 | semidirect |
| 63. C2×C167⋊C8 | D4 | semidirect |
| 86. M16×C167 | D4 | semidirect |
| 148. C167 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D167 | semidirect |
| 226. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128865 | 2 |
| C2×#19128852 | 2 |
| C22×#14581938 | 2 |
| #24923840 | 2 |
| #24923836 | 2 |
| #24923660 | 2 |
| #24923657 | 2 |
| #24923652 | 2 |
| #24923640 | 2 |
| #24923227 | 2 |
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #3154 | 167 |